Theorems · Theorem · commutative algebra
IsRegular.right
∀ {R : Type u_1} [inst : Mul R] {c : R}, IsRegular c → IsRightRegular cA regular element c is right-regular
- Defined in
- Mathlib.Algebra.Regular.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsRegularstatement and proof · cited by 116
- IsRightRegularstatement · cited by 93
Cited by19
Results whose statement or proof uses this declaration.
- IsRegular.starproof · cited by 5
- IsRegular.powproof · cited by 3
- Polynomial.Sequence.span_degreeLTproof · cited by 3
- IsRegular.mem_nonZeroDivisorsproof · cited by 2
- IsRegular.prodproof · cited by 2
- star_left_conjugate_lt_conjugateproof · cited by 2
- Submonoid.LocalizationMap.isCancelMulZeroproof · cited by 2
- isRightRegular_of_mul_eq_oneproof · cited by 2
- IsArtinianRing.isUnit_iff_isRegular_of_mulOppositeproof · cited by 2
- isRegular_mul_and_mul_iffproof · cited by 2
- IsLocalizedModule.linearIndependent_liftproof · cited by 2
- Matrix.vecMul_injective_of_isUnitproof · cited by 2